6.18.16 problem section 9.2, problem 16

Internal problem ID [2130]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 16
Date solved : Tuesday, September 30, 2025 at 05:24:17 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=14 \\ y^{\prime \prime }\left (0\right )&=-40 \\ \end{align*}

✓ Maple. Time used: 0.057 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-diff(y(x),x)-3*y(x) = 0; 
ic:=[y(0) = 0, D(y)(0) = 14, (D@@2)(y)(0) = -40]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -5 \,{\mathrm e}^{-3 x}+2 \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 25

ode=D[y[x],{x,3}]+3*D[y[x],{x,2}]-D[y[x],x]-3*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==14,Derivative[2][y][0] ==-40}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -5 e^{-3 x}+3 e^{-x}+2 e^x \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) - Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 14, Subs(Derivative(y(x), (x, 2)), x, 0): -40} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 e^{x} + 3 e^{- x} - 5 e^{- 3 x} \]